## Tuesday, December 10, 2013

### Answer to one mathleague quesiton from AoPS

Question is here.

You have two congruent triangles. 17-same angle and- x (SAS)
Using distance formula, the two green lines are of the same length.
$$\left( a-25\right) ^{2}+\left( 20-15\right) ^{2}=a^{2}+20^{2}$$
a = 5

Use another distance formula to get x -- the blue line.
$$\sqrt {\left( 5-17\right) ^{2}+20^{2}}=\sqrt {544}= 4\sqrt {34}$$